The C-space is the space of all possible configurations of a robot. Two somewhat different spaces of interest are the task space and the workspace.

The task space is a space in which the robot's task can be naturally expressed. For example, if the task is to control the position of the tip of a marker on a board, then task space is the Euclidean plane. If the task is to control the position and orientation of a rigid body, then the task space is the 6-dimensional space of rigid body configurations. You only have to know about the task, not the robot, to define the task space.

The workspace is a specification of the configurations that the end-effector of the robot can reach, and has nothing to do with a particular task. For example, a planar robot with 2 revolute joints, limited to ranges of motion of 180 and 150 degrees, has the workspace shown here. The workspace is often defined in terms of the Cartesian points that can be reached by the end-effector, but it is also possible to include the orientation. The set of positions that can be reached with all possible orientations is sometimes called the dexterous workspace.

So this concludes Chapter 2 on configuration spaces. In Chapter 3, we will focus on representing configurations and velocities of rigid bodies.